Point from @kiamlaluno is correct, the apachesolr_stats has apachesolr listed as a dependency. Therefore, in order to disable the apachesolr, you should first disable the apachesolr_stats (and possibly other dependent modules).
I suspect that this issue comes from cached blocks, when I look at the trace you posted. Try to clear the cache and/or disable the apachesolr_stats block before trying to disable the apachesolr module.
You should try to disable the apachesolr_stats module first. If you are using drush, this would be the command:
drush dis -y apachesolr_stats
If you don't have drush, you can also use MySQL/PHPMyAdmin commands, here are some links with examples:
How do I clear cache using an SQL query? [if that answer works for you, you can upvote ;) ] https://www.drupal.org/documentation/clearing-rebuilding-cache